Post on 16-Oct-2019
transcript
Hadroquarkonium from Lattice QCD
Gunnar Bali
with Maurizio Alberti, Sara Collins, Francesco Knechtli, Graham Moir,Wolfgang Söldner
Wuppertal – Regensburg – Cambridge
Symposium on EFTs and LGT TUM IAS, May 21, 2016
Outline
MotivationHadroquarkoniumLattice simulationSummary
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 2 / 21
Recent charmonium spectrum resultsHPQCD [arXiv:1411.1318] ETMC [arXiv:1510.07862]
0−+ 1−− 1+− 0++ 1++
JPC
3.0
3.2
3.4
3.6
3.8
Mas
s/
GeV χc0
χc1
ηc
η′c
hc
J/Ψ
Ψ′
expt (PDG)
m`/ms = 1/5
m`/ms = 1/10
m`/ms = phys
1
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
0−+
0++
1−−
1++
1+−
2++
2−+
2−−
3−−
ηc χc0 J/Ψ χc1 hc χc2 ηc2 Ψ2
meson m
ass in G
eV
A1T1
ET2
exp.
χQCD [arXiv:1410.3343]
0.6
0.8
1
1.2
1.4
1.6
r0(fm) mc ms MJ/ψ-Mηc
Mχc0
Mχc1
MhcfDs
Ratio
1.09(3)0.095(5)
0.1132(7)3.41475(31)
3.51066(7)3.52541(16)
0.2575(46)
0.465(10)1.118(25)
0.101(7)0.119(7)
3.439(44)3.524(66)
3.518(71)0.2536(43)
Exp (PDG)this work (MDs
, MDs* and MJ/ψ as Input)
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 3 / 21
However ∃ many states near thresholds
1974 – 1977: 10 cc̄ resonances, 1978 – 2001: 0 cc̄’s2002 – 13: ≤ 12 new cc̄’s found by BaBar, Belle, CLEO-c, CDF, D0
4.6
4.4
4.2
4.0
3.8
3.6
3.4
3.2
3.0
L = 2L = 1L = 0
m/G
eV
ηc
J/ψ
ψ(2S)
ψ(4040)
ψ(4415)
χc
ψ(3770)
ψ(4160)
ηc(2S)
hc
Y(4260)
X(3871/3875)X(3943)
Y(3940)Z(3934)
Y(4660)
Y(4350)
X(4160)
DD
DD*
D*D
*
DD**
DsDs
DsDs* Ds
*Ds
*
---
-
-- -
Z+(4430)
standard?????
new detectorshigher luminositynew channels:
B decaysγγ
ψψ-productiongg in pp collisions.Will there be pp̄?Discoveries at LHC!cq̄qc̄ ?cgc̄ hybrids ?
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 4 / 21
Near threshold states and resonancesMultihadron channels need to be included!Recent studies, open charm:
D∗s0(2317) [DK ] JP = 0+, Ds1(2460) [D∗K ] JP = 1+ Lang et al.
[1403.8103]D∗
0 (2400) [D̄π] JP = 0+, D1(2430) [D̄∗π] JP = 1+, Mohler et al.[1208.4059]
Hidden charm:ψ(3770) JPC = 1−−, χc0(2P) JPC = 0++ [D̄D] Lang et al. [1503.05363].X (3872) I = 0 [DD̄∗, J/ψω] JPC = 1++, Prelovsek et al. [1307.5172],DeTar et al. [1411.1389], update in [1508.07322].X (3872) I = 1 [DD̄∗, J/ψρ, (c̄ d̄)(cu)] JPC = 1++ Padmanath et al.[1503.03257], no candidate found.Y (4140) [J/ψφ, DsD̄∗
s , (c̄ s̄)(cs)] JPC = 1++ channel Padmanath et al.[1503.03257], s- and p-wave scattering Ozaki et al. [1211.5512], nocandidate found.Zc(3900)+ [J/ψπ, DD̄∗, ηcρ, . . . ] IG (JP) = 1+(1+), Prelovsek et al.[1405.7623], Lee et al. [1411.1389], no candidate found.
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 5 / 21
Zc(3900)+, IG(JP) = 1+(1+)
Prelovsek et al. [1405.7623]
Lattice
D(2) D*(-2)
D*(1) D*(-1)
J/ψ(2) π(−2)ψ
3 π
D(1) D*(-1)ψ
1Dπ
D* D*η
c(1)ρ(−1)
ψ2S
π
D D*j/ψ(1) π(-1)η
c ρ
J/ψ π
Exp.
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6
E[G
eV]
Even in this “simple” casewhere the minimal configu-ration consists of four quarksand mixing with standardcharmonia can be excluded,a huge number of channelsneeds to be considered!
Basis of 22 operators: no candidate for a Z+c found below 4.2 GeV.
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 6 / 21
LHCb: pentaquarks are back
[GeV]pψ/Jm4 4.2 4.4 4.6 4.8 5
Eve
nts/
(15
MeV
)
0
100
200
300
400
500
600
700
800
LHCb(b)
Re A
-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.1
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
LHCb
(4450)cP
(a)
15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
(4380)cP
(b)
Pc Re APc
Im A
P c
P+c (4380) (JP = 3
2−) and P+
c (4450) (JP = 52+) from Λb → J/ψpK
[LHCb: R. Aaij et al, 1507.03414].
Conjecture of attractive forces between charmonium and pp systems:[S. Brodsky, I. Schmidt, G. de Teramond, PRL64 (90) 1011].
Many interpretations, pre- and post-dictions (190 citations).
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 7 / 21
5 quark (4 q, 1 q̄) systems are very difficult to study directly on thelattice, in particular if many decay channels are possible.
What about testing a particular model instead?Hadroquarkonia: [S. Dubynskiy, M. Voloshin 0803.2224]: Quarkoniabound within ordinary hadrons.
Many combinations of baryon plus charmonium are close-by. Examples:
JP = 32
−: m(∆) + m(J/ψ) ≈ 4329MeV vs. 4380MeV (width 200MeV).
JP = 52+: m(N) + m(χc2) ≈ 4496MeV vs. 4450MeV (width 40MeV).
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 8 / 21
Quarkonia and potentialsmQ,mQv � ΛQCD, v � 1 −→ Non-relativistic approach (pNRQCD):
Hψnlm = Enlψnlm , H = 2(mQ − δmQ) +p2
mQ+ V0(r) + · · ·
-1.5
-1
-0.5
0
0.5
1
1.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
V(r
)/G
eV
r/fm
Σu-
Πu
Σg+
V0(r) can be computed on thelattice.(also 1/mQ and 1/m2
Q correc-tions)
Does this apply to charmonia?Is v . 0.5� 1?Is mcv ≈ 600MeV� ΛQCD?
Nevertheless, we can say some-thing about bottomonia andprovide guidance for charmonia.
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 9 / 21
Hadroquarkonia in the static limitThis particular picture can be tested in the static limit.Does the static potential V0(r) become more or less attractive in thebackground of a light hadron?
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ttδ tδ
r
Create a zero-momentum projected hadronic state |H〉 at the time 0.Let it propagate to δt, create a quark-antiquark “string”.Destroy this at t + δt and the light hadron at t + 2δt.In the limit t →∞ compute
∆VH(r , δt) = VH(r , δt)− V0(r)
and extrapolate δt →∞.Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 10 / 21
CLS Ensembles
Nf = 2 + 1 CLS ensembles with 2m` + ms = const.(∃ additional sets with m̃s = const and m` = ms)
150
200
250
300
350
400
450
0 0.002 0.004 0.006 0.008 0.01
physical
U103H101
U102H102
U101H105N101
S100C101D101
D150
H402H400B450
S400
N401
H200N202
N203
S201N200
D200
N300N301
N302
J303
J500
J501
mπ[M
eV]
a2[fm2]
U: 128× 243
B: 64× 323
H: 96× 323
S: 128× 323
C: 96× 483
N: 128× 483
D: 128× 643
J: 192× 643
CLS: HU Berlin, TC Dublin, UA Madrid, Mainz, Milano Bicocca,Regensburg, Roma I, Roma II, Wuppertal, DESY Zeuthen
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 11 / 21
Lattice details
We want a large volume that comfortably accommodates the hadron.
We wish to go to realistically light quark masses but not too light sincethen correlation functions can become noisy and statistically lessmeaningful.
Nf = 2 + 1 CLS ensemble C101 (96× 483 sites):
Mπ = 220MeV, MK = 470MeV, LMπ ≈ 4.6, L ≈ 4.1 fm, a ≈ 0.086 fm.
High statistics: 1552 configs, separated by 4 MDUs, times 12 hadronsources (1 forward, 1 backward, 10 forward and backward propagating ⇒22 2-point functions). Wilson loops at all positions and in all directions.
Wilson loops are optimized using four smearing levels and ground stateoverlap of the hadronic two-point function is optimized too.
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 12 / 21
QQ binding energy shift “within” a pion
[M. Alberti et al, PRELIMINARY]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−6
−5
−4
−3
−2
−1
0
r [fm]
∆VΠ(r
)[M
eV]
Π
Preliminary
δ t = 0
δ t = 3
δ t = 6
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 13 / 21
Within a kaon
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−7
−6
−5
−4
−3
−2
−1
0
r [fm]
∆V
K(r
)[M
eV]
K
Preliminary
δ t = 0
δ t = 3
δ t = 6
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 14 / 21
Within a φ
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−9
−8
−7
−6
−5
−4
−3
−2
−1
0
r [fm]
∆V
φ(r
)[M
eV]
φ
Preliminary
δ t = 0
δ t = 3
δ t = 6
Here we have to be careful with polarizations!
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 15 / 21
QQ binding energy shift “within” a nucleon
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−7
−6
−5
−4
−3
−2
−1
0
r [fm]
∆V
N+(r
)[M
eV]
N+
Preliminary
δ t = 0
δ t = 3
δ t = 6
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 16 / 21
Within a cascade
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−7
−6
−5
−4
−3
−2
−1
0
r [fm]
∆VΞ
+(r
)[M
eV]
Ξ+
Preliminary
δ t = 0
δ t = 3
δ t = 6
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 17 / 21
... and negative parity
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7−8
−7
−6
−5
−4
−3
−2
−1
0
r [fm]
∆VΞ
−(r
)[M
eV]
Ξ−
Preliminary
δ t = 0
δ t = 3
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 18 / 21
Within a decuplet cascade
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−12
−10
−8
−6
−4
−2
0
r [fm]
∆VΞ
∗+(r
)[M
eV]
Ξ*+
Preliminary
δ t = 0
δ t = 3
δ t = 6
Again we have to be careful with the helicity!Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 19 / 21
What does this mean?In the absence of a light hadron the slope of V0 is ≈ 1GeV/ fm.Within VH this is reduced by ≈ 3MeV/(0.5 fm) ≈ 6%�.The heavy quarks are a bit weaker bound but is there any energy gain?
Virial theorem for a purely linear potential V (r) = σr :
2〈T 〉 =
⟨r dV
dr
⟩= σ〈r〉 = 2E − 2〈V 〉 = 2E − 2σ〈r〉
This means 〈r〉 = 2E/(3σ). Feynman-Hellmann:
∂E∂σ
=
⟨∂H∂σ
⟩= 〈r〉 =
2E3σ
=⇒ E (σH) = E (σ0) + (σH − σ)∂E∂σ
∣∣∣∣σ=σ0
=
(1 + 2σH
σ0
) E (σ0)
3A 6%� smaller σ gives a 4%� smaller energy (adding to 2mQ). The realworld effect is smaller as the potential also contains a Coulomb term.So this amounts to |∆E | = 1–2MeV.
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 20 / 21
Summary and Outlook
Heavy quark states are narrower and cleaner than many light quarkresonances. Theoretically, the heavy quark limit provides guidance.This is a prime arena for addressing “exotic” spectroscopy.Threshold states with hidden charm or bottom are a huge challenge,however, some aspects can be addressed within approximationsand/or model assumptions.Pentaquarks are back! For how long?Modifications of the static potential in the presence of light hadronsappear tiny (similarly small as in the deuteron). Is this the end ofhadro-quarkonia?Interestingly, there appears to be similar attraction in all of thechannels investigated so far.
Gunnar Bali (Regensburg) Hadroquarkonium TUM IAS 21.5.2016 21 / 21